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1 Supplementary Figure 1 Illustrative example of ptdt using height The expected value of a child s polygenic risk score (PRS) for a trait is the average of maternal and paternal PRS values. For example, if a mother s PRS is A, the expected PRS of an egg, which contains half of the maternal genetic material, is A/2. If the father s PRS is B, the expected PRS of a sperm is B/2. The expected value of the child s PRS is then (A + B)/2. (a) In a randomly selected cohort of parent child trios, the average of the children s PRSs for height, in light blue, is expected to equal the average of the mid-parent PRS for height, in dark blue; for each pair of parents, the mid-parent PRS is calculated by averaging the maternal and paternal PRSs; the variance of the mid-parent PRS is reduced because it is the average of the maternal and paternal values. (b) In a cohort of trios phenotypically selected for very high height in the offspring (offspring who are taller than expected based on the height of the parents), we expect offspring PRS to exceed mid-parent PRS. The difference between the mean of the offspring PRS distribution and mid-parent PRS distribution, n, we refer to as polygenic transmission disequilibrium. 1

2 Supplementary Figure 2 ASD probands of European ancestry over-inherit ASD-associated polygenic risk. We performed ptdt after restricting the cohort to European ancestry (Supplementary Note; n = 1,851 SSC probands, n = 3,209 PGC ASD probands, n = 5,060 SSC and PGC ASD probands combined, n = 1,509 SSC unaffected siblings). Transmission disequilibrium is shown in terms of standard deviations on mid-parent distribution ± 1.96 standard error (95% confidence interval). P values denote the probability that the mean of the ptdt deviation distribution is 0 (two-sided, one-sample t test). 2

3 Supplementary Figure 3 Polygenic risk for schizophrenia stratifies by ancestry. See the Supplementary Note for discussion of ancestral stratification of schizophrenia polygenic risk score. 3

4 Supplementary Figure 4 Large de novo deletions and de novo deletions in constrained genes were associated with ASD case status. Constrained genes are intolerant of heterozygous loss-of-function variations (probability of being loss-of-function intolerant (pli) 0.9); P values are from Fisher s exact test and estimate the probability with which the variant type is equally likely to be seen in cases (n = 2,587 subjects) and controls (n = 2,100 subjects); error bars are ±1 standard error. 4

5 Supplementary Figure 5 Unconstrained de novo deletions were not associated with ASD case status. Contributing deletions are deletions in either category in Supplementary Figure 4 (constrained or 500 kb and unconstrained); error bars are ±1 standard error; P values are from Fisher s exact tests and estimate the probability that the variant type is equally likely to be seen in cases (n = 2,587 subjects) and controls (n = 2,100 subjects). 5

Supplementary Figure 6 Ancestry of Simons Simplex Collection probands Included/excluded denotes whether the first two proband principal components of ancestry were within the study-defined bounds of

6 Supplementary Figure 6 Ancestry of Simons Simplex Collection probands Included/excluded denotes whether the first two proband principal components of ancestry were within the study-defined bounds of European ancestry; HapMap population CEU, individuals of Northern and Western European ancestry residing in Utah, USA; HapMap population TSI, Tuscans in Italy; non-european, all HapMap cohorts excluding CEU and TSI; see the Online Methods for more information. 6

7 Supplementary Figure 7 Ancestry of parents of ASD probands in the Psychiatric Genomics Consortium Autism Group. Included/excluded denotes whether the first two parent principal components of ancestry were within the study-defined bounds of European ancestry; families were marked as European ancestry if both parents were marked as included; HapMap population CEU, individuals of Northern and Western European ancestry residing in Utah, USA; HapMap population TSI, Tuscans in Italy; non- European, all HapMap cohorts excluding CEU and TSI; see the Online Methods for more information. 7

8 Supplementary Figure 8 Association between constrained PTV rate and proband IQ in SSC. The red line denotes the linear relationship between contributing PTVs (Online Methods) and full-scale IQ in SSC probands (n = 2,492 subjects); the blue line denotes the linear relationship between all other PTVs and full-scale IQ in SSC probands (n = 2,492 subjects). Shaded regions denote 95% confidence intervals. The red line P value is associated with a Poisson regression predicting count of contributing de novo PTVs from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of contributing de novo PTVs; the blue line P value is associated with a Poisson regression predicting count of non-contributing de novo PTVs from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of non-contributing de novo PTVs. Control rate dots were calculated from n = 1,902 unaffected sibling controls. 8

9 Supplementary Figure 9 Association between contributing deletions and proband IQ in SSC. The red line denotes the linear relationship between rate of contributing deletions (Online Methods) and full-scale IQ in SSC probands (n = 2,581 subjects); the blue line denotes the linear relationship between all other de novo deletions and full-scale IQ in SSC probands (n = 2,581 subjects). Shaded regions denote 95% confidence interval. The red line P value is associated with a Poisson regression predicting count of contributing de novo deletions from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of contributing de novo deletions; the blue line P value is associated with a Poisson regression predicting count of non-contributing de novo deletions from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of non-contributing de novo deletions. Control rate dots were calculated from n = 2,100 unaffected sibling controls. 9

$Supplementary Figure 10 De novo deletions, but not duplications, in constrained genes were associated with ASD. Rates are the fraction of CNVs that include a constrained gene.$

10 Supplementary Figure 10 De novo deletions, but not duplications, in constrained genes were associated with ASD. Rates are the fraction of CNVs that include a constrained gene. P values are from Fisher s exact tests and estimate the probability with which case (n = 82 with duplication, n = 116 with deletion) and control (n = 27 with duplication, n = 45 with deletion) carriers are equally likely to have a deletion that includes a constrained gene. 10

11 Supplementary Figure 11 Association between CDNV rate and proband IQ in SSC. The red line denotes the linear relationship between the rate of CDNVs (contributing de novo variants; Online Methods) and full-scale IQ in SSC probands (n = 2,340 subjects); the blue line denotes the linear relationship between all other de novo deletions and PTVs and full-scale IQ in SSC probands (n = 2,340 subjects). Shaded regions denote 95% confidence intervals. The red line P value is associated with a Poisson regression predicting count of CDNVs from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of CDNVs; the blue line P value is associated with a Poisson regression predicting count of non-cdnv de novo deletions and PTVs from proband IQ and proband sex and estimates the probability of no association between proband IQ and the rate of non-cdnv de novo deletions and PTVs. Control rate dots were calculated from n = 1,736 unaffected sibling controls. 11

12 Supplementary Figure 12 Association between the male:female carrier ratio and de novo variant category. P values were generated using Fisher s exact tests and estimate the probability that there is no difference between male proband (n = 2,029) and female proband (n = 317) variant rates; see the Online Methods for variant description. 12

13 Supplementary Tables Supplementary Table 1. Description of analytic cohorts Cohort Cohort description All members genotyped Subset with exome sequence for both parents and proband Subset with exome sequence for both parents, proband and sibling SSC quads 2,091 1,896 (90.7%) 1,729 (82.7%) SSC European ancestry SSC quads 1,509 1,366 (90.5%) 1,221 (80.9%) SSC trios (91.1%) NA European ancestry SSC trios (90.9%) NA PGC ASD trios 3,870 NA NA PGC ASD European ancestry PGC ASD trios 3,209 NA NA Ancestry derived from analysis of genetic data (Online Methods: Sample Description); trio families included both parents and the proband; quad families included both parents, the proband, and an unaffected sibling; count of families with all members genotyped refers to those remaining after imputation and data cleaning using the Ricopili pipeline 1.

14 Supplementary Table 2. Description of PGC ASD subcohorts PGC ASD Cohort Number of genotyped trios Probands of European ancestry (%) Reference for proband IQ measurement Autism Center of Martin et al. 2 Excellence, UCLA Children s Hospital of Philadelphia Autism Genome 1, Anney et al. 3 Project (Group 1) Autism Genome Project (Group 2) Johns Hopkins University IQ measure not collected Montreal/Boston Collection Total 3, Ancestry derived from analysis of genetic data (Online Methods: Sample Description); see PGC Cross Disorders 2013 for more details about cohorts 4 ; count of trios refers to those with all members remaining after imputation and data cleaning in the Ricopili pipeline 1. 2

15 Supplementary Table 3. Description of summary statistics from genome-wide association studies Phenotype Data source Discovery sample size P-value threshold for SNP inclusion in PRS SNPs included in PGC ASD + SSC PRS SNPs included in SSConly PRS Availability of summary statistics Autism spectrum disorder (ASD) ipsych-broad Autism 5 7,783 Cases, 11,359 Controls ,634 28,552 Pre-publication consortium data; mjdaly@atgu.mgh.harvard.edu or anders@biomed.au.dk for more information Educational attainment (EA) Discovery and replication metaanalysis, 23andMe excluded 6 328,917 Individuals 1 155, ,851 Summary statistics publically available from Okbay et al. Schizophrenia (SCZ) PGC ,989 Cases, 113,075 Controls ,516 24,808 Summary statistics publically available from the Schizophrenia Working Group of the Psychiatric Genomics Consortium Body mass index (BMI) GIANT Consortium 8 (European metaanalysis) 322,154 Individuals ,492 NA Summary statistics publically available from the GIANT Consortium SNPs excluded from PRS with SSC/PGC ASD imputation info score < 0.6; see Online Methods: Polygenic Risk Scoring for overview of summary statistics in the context of polygenic risk scoring. 3

16 Supplementary Table 4. Estimates of assortative mating from polygenic risk scores in SSC and PGC ASD Cohort (European ancestry) ASD PRS (r, p-value) SSC (7.13E-03) PGC ASD (0.78) EA PRS (r, p-value) (0.49) (1.36E-04) SCZ PRS (r, p-value) (0.94) (0.036) R-values are Pearson correlation coefficients between maternal and paternal PRS within either SSC (n = 1,851 families) or PGC ASD (n = 3,209 families) for a given PRS with the first 10 principal components of ancestry regressed out (e.g., correlation between SSC mother ASD PRS and SSC father ASD PRS); p-values are the probability that there is no correlation between paternal and maternal PRS; analysis restricted to European ancestry families, with ancestry derived from analysis of genetic data (Online Methods: Sample Description). 4

17 Supplementary Table 5. Correlations between PRS in SSC and PGC ASD Probands Mothers Fathers SSC PGC ASD ASD PRS EA PRS ASD PRS EA PRS EA PRS r = 7.8E-03 n = 1,852 r = , n = 3,209 P = 0.74 P = 0.56 SCZ PRS r = 0.021, r = 0.015, r = 5.5E-03, r = 0.036, P = 0.36 P = 0.53 P = 0.75 P = EA PRS r = 0.025, n = 1,852 r = -2.4E-03, n = 3,209 P = 0.28 P = 0.89 SCZ PRS r = 0.016, r = 0.035, r = 0.025, r = 0.012, P = 0.50 P = 0.13 P = 0.15 P = 0.48 EA PRS r = 0.050, n = 1,851 r = , n = 3,209 P = P = 0.44 SCZ PRS r = 4.0E-04, r = -1.5E-03, r = -4.0E-03, r = 0.015, P = 0.99 P = 0.52 P = 0.82 P = 0.40 R-values are Pearson correlation coefficients; analysis performed in European ancestry cohorts of SSC and PGC ASD, with ancestry derived from analysis of genetic data (Online Methods: Sample Description); first 10 principal components of ancestry regressed out of PRS (e.g., proband principal components of ancestry regressed out of proband PRS before analysis); p- values are the probability there is no correlation between the polygenic risk scores. 5

18 Supplementary Table 6. Parent PRS as a function of parent sex Parent Sex (father = 1, mother = 0) n families (European ancestry) ASD EA SCZ PRS PRS PRS Beta p-value Beta p-value Beta p-value SSC 1, PGC ASD 3, Effect size and p-values generated from three separate linear regressions predicting PRS from parent sex while controlling for the first 10 principal components of mother and father ancestry; p-value is the probability the means of the mothers and fathers PRS distributions are equal; ancestry derived from analysis of genetic data (Online Methods: Sample Description). 6

19 Supplementary Table 7. Mid-parent PRS as a function of proband sex Proband Sex (male = 1, female = 0) n families (European ancestry) Midparent ASD PRS Midparent EA PRS Midparent SCZ PRS Beta p-value Beta p-value Beta p-value SSC 1, E PGC ASD 3, E Effect size and p-values generated from three separate linear regressions predicting mid-parent PRS from proband sex while controlling for 10 principal components of proband ancestry; p- value is the probability that mid-parent PRS does not differ by proband sex; ancestry derived from analysis of genetic data (Online Methods: Sample Description). 7

20 Supplementary Table 8. ASD Probands Over Inherit ASD Associated Polygenic Risk Ancestry Restriction None European Ancestry Cohort SSC Probands (n = 2,584) SSC Siblings (n = 2,091) PGC ASD Probands (n = 3,870) SSC+PGC ASD Probands (n = 6,454) SSC Probands (n = 1,851) SSC Siblings (n = 1,509) PGC ASD Probands (n = 3,209) SSC+PGC ASD Probands (n = 5,060) ASD PRS (ptdt deviation mean (SD), p-value) EA PRS (ptdt deviation mean (SD), p-value) SCZ PRS (ptdt deviation mean (SD), p-value) 0.11 (0.96), 4.47E (0.68), 1.32E (0.37), 7.61E (0.96), (0.63), (0.36), (1.02), 9.07E (0.74), 1.86E (0.52), 3.25E (0.99), 2.97E (0.70), 1.41E (0.44), 1.35E (0.98), 2.27E (0.86), 4.63E (0.94), 1.94E (0.96), (0.81), (0.92), (1.03), 2.39E (0.87), 1.11E (0.92), 1.66E (1.01), 2.76E (0.87), 2.40E (0.93), 2.12E-13 P-values denote the probability that the mean of the ptdt deviation distribution is 0 (twosided, one-sample t test); ancestry derived from analysis of genetic data (Online Methods: Sample Description). 8

21 Supplementary Table 9. BMI ptdt analysis SSC Probands (n = 2,584) SSC Siblings (n = 2,091) PGC ASD Probands (n = 3,870) BMI PRS (ptdt deviation mean (SD), p-value) 8.2E-03 (0.38), E-03 (0.39), (0.51), 0.12 P-values denote the probability that the mean of the ptdt deviation distribution is 0 (twosided, one-sample t test). 9

22 Supplementary Table 10. Comparison between ptdt deviation in discovery (SSC) and replication (PGC ASD) cohorts ASD PRS ptdt EA PRS ptdt SCZ PRS ptdt No ancestry P = 0.67 P = 0.89 P = 0.08 restriction European ancestry P = 0.83 P = 0.89 P = 0.39 P-values were derived from two-sided, two-sample t tests and reflect the probability that the means of the ptdt deviation distributions in Supplementary Table 8 in SSC and PGC ASD are equal; number of subjects in each comparison available from Supplementary Table 8; ancestry derived from analysis of genetic data (Online Methods: Sample Description). 10

23 Supplementary Table 11. ptdt analysis in probands with and without intellectual disability Cohort ID status ASD PRS (ptdt deviation mean (SD), p-value) SSC With ID (n = 783) 0.13 (0.95), 9.15E-05 Without ID (n = 1,795) 0.10 (0.97), 1.06E-05 PGC ASD With ID (n = 558) 0.16 (1.08), 4.65E-04 Without ID (n = 948) 0.13 (0.98), SSC + PGC ASD 3.94E-05 With ID (n = 1,341) 0.14 (1.00), 1.50E-07 Without ID (n = 2,743) 0.11 (0.97), 2.23E-09 EA PRS (ptdt deviation mean (SD), p-value) (0.62), 1.36E (0.68), 2.24E (0.78), 9.46E (0.77), 1.71E (0.67), 5.50E (0.71), 5.02E-10 SCZ PRS (ptdt deviation mean (SD), p-value) (0.32), 1.20E (0.40), 1.87E (0.53), (0.64), (0.37), 1.69E (0.45), 2.17E-05 P-values denote the probability that the mean of the ptdt deviation distribution is 0 (twosided, one-sample t test); ID (intellectual disability) = full-scale IQ < 70 (Online Methods: ptdt). 11

24 Supplementary Table 12. Comparison between ptdt deviation in SSC + PGC ASD with and without ID ASD PRS ptdt EA PRS ptdt SCZ PRS ptdt SSC + PGC ASD P = 0.32 P = 0.47 P = 0.94 P-values were derived from two-sided, two sample t tests and reflect the probability that the means of the ptdt deviation distributions in SSC + PGC ASD with (n = 1,341) and without ID (n = 2,743) are equal (Supplementary Table 11). 12

25 Supplementary Table 13. ptdt in SSC probands with and without de novo mutations Probands with CDNV (n = 221) Probands without CDNV (n = 2,124) ID probands without CNV or PTV (n = 533) Probands with constrained PTV and/or any CNV (n = 318) Probands without constrained PTV and/or any CNV (n = 2,028) ASD PRS (ptdt deviation mean (SD), p-value) EA PRS (ptdt deviation mean (SD), p-value) SCZ PRS (ptdt deviation mean (SD), p-value) 0.17 (1.04), (0.70), (0.32), (0.95), 1.14E (0.66), 2.02E (0.37), 3.87E (0.93), 5.14E (0.63), 1.64E (0.30), 1.13E (0.98), 1.66E (0.69), (0.36), (0.96). 7.83E (0.66), 4.35E (0.36), 2.51E-05 See Online Methods: ptdt for CDNV definition; all variants are de novo; constrained PTV = protein truncating variant that was not observed in the publically available ExAC database and affected a gene with a high probability of being loss-of-function intolerant (pli 0.9); P-values denote the probability that the mean of the ptdt deviation distribution is 0 (two-sided, onesample t test); ID (intellectual disability) = full-scale IQ <

26 Supplementary Table 14. Prevalence of classes of de novo variation in SSC Variant class n cases with n controls with OR p-value variant (% cases) variant (% controls) Constrained deletions 57/2,587 (2.2%) 10/2,100 (0.5%) E-07 Large unconstrained 8/2,587 (0.3%) 1/2,100 (0.05%) deletions Contributing CNV 65/2,587 (2.5%) 11/2,100 (0.5%) E-08 deletions Non-contributing 43/2,587 (1.7%) 29/2,100 (1.4%) deletions Contributing PTVs 167/2,346 (7.1%) 37/1,736 (2.1%) E-14 Non-contributing PTVs 182/2,346 (7.8%) 120/1,736 (6.9%) CDNVs 221/2,346 (9.4%) 45/1,736 (2.6%) E-20 CNV = copy number variant; PTV = protein truncating variant (frameshift, splice acceptor, splice donor, nonsense); constrained deletions = deletions containing a gene that was predicted to be intolerant of heterozygous loss of function variation (probability of being loss-of-function intolerant (pli) 0.9); large unconstrained deletions = deletions 500 kb that do not contain a gene predicted to be intolerant of heterozygous loss of function variation; contributing CNV deletions = either 1) constrained deletion or 2) large unconstrained deletion; non-contributing deletions = de novo deletions that were neither constrained nor large unconstrained; contributing PTV = variant that was not observed in the publically available ExAC database and affected a gene with a high probability of being loss-of-function intolerant (pli 0.9); non-contributing PTV = de novo PTV that is not contributing; CDNV = either contributing CNV deletion or contributing PTV; deletions roster was genotyped SSC probands and siblings; PTV and CDNV roster was genotyped and sequenced SSC probands and siblings; OR = odds ratio from case-control Fisher s Exact test; p-values generated from Fisher s Exact test indicate probability that the variant class is equally likely to be seen in cases and controls. 14

27 Supplementary Table 15. Relationship between rate of CDNVs and adverse co-occurring neurodevelopmental outcomes Number of probands in category (SSC prevalence of phenotype) Motor delay Seizures ID No co-occurring outcomes 147 (6.3%) 183 (7.8%) 705 (30.2%) 1,476 Count of CDNVs CDNV rate (p-value controlling for proband sex) 0.26 (2.57E-08) 0.18 (3.8E-04) 0.13 (6.4E-03) CDNV rate was calculated by dividing the count of CDNVs in a category by the number of probands in the category; p-values were from Poisson regression predicting CDNV count from present/absence of each co-occurring neurodevelopmental outcome and proband sex, and estimate the probability that the rate of CDNVs in a co-occurring outcome category was equal to the rate in probands with no co-occurring outcomes; motor delay was walking unaided at or after 19 months after birth; ID = intellectual disability = full-scale IQ < 70; CDNVs = contributing de novo variants (Online Methods: De novo variant analyses); analytic cohort included SSC probands who were both genotyped and sequenced. 15

28 Supplementary Table 16. CDNV male:female ratio grouped by adverse co-occurring neurodevelopmental outcomes Count of cooccurring neurodevelopmental outcomes in probands Number of probands in co-occurring neurodevelopmental category (Number of probands in category with CDNV) Proband CDNV rate (OR, p- value a ) 0 1,476 (105) (3.15, 3.88E-10) (77) 0.11 (4.53 (5.53E-15) (33) 0.25 (10.18, 6.94E-23) 3 16 (6) 0.38 (15.05, 9.08E-10) Observed male:female proband CDNV carrier ratio (Expected male:female proband ratio) / (observed male:female proband CDNV carrier ratio) (p-value b ) (0.095) (6.81E-04) (1.57E-03) (2.87E-03) Co-occurring neurodevelopmental outcomes (delayed walking, intellectual disability, seizures) are described in Online Methods: De novo variant analyses, as are CDNVs; observed male:female ratio is the ratio of male:female CDNV carriers within a given outcome category; proband CDNV rate is the count of CDNVs in probands in each outcome category divided by count of probands in the outcome category; odds ratio (OR) was calculated from Poisson regression predicting CDNV count from case/control status for all controls (n = 1,736) and cases in the outcome category, controlling for maternal and paternal age at birth of the child; a p-value is derived from the Poisson regression and estimates the probability that the proband CDNV rate is equal to the control CDNV rate (CDNV rate in 1,736 SSC controls is variants/exome); b p-value was calculated using a Fisher s exact test and estimates probability that the expected male:female proband ratio in SSC (overall SSC ratio of probands who were both genotyped and sequenced, (6.42)) was equal to the observed male:female proband ratio of CDNV carriers in the co-occurring neurodevelopmental outcome category. 16

29 Supplementary Table 17. ptdt as a function of adverse co-occurring neurodevelopmental outcomes Adverse co-occurring neurodevelopmental outcome category Probands in category ASD PRS (ptdt deviation mean (SD), p-value) 0 1, (0.96), 3.00E (0.97), 4.75E-05 EA PRS (ptdt deviation mean (SD), p-value) (0.68), 2.02E (0.65), 2.59E-04 SCZ PRS (ptdt deviation mean (SD), p-value) (0.41), 5.75E (0.32), 4.58E-05 Co-occurring neurodevelopmental outcomes (delayed walking, intellectual disability, seizures) are described in Online Methods: De novo variant analyses; analytic cohort is genotyped and sequenced SSC probands with ptdt available; P-values denote the probability that the mean of the ptdt deviation distribution is 0 (two-sided, one-sample t test). 17

30 Supplementary Table 18. Distinct polygenic risk factors are independently over transmitted to ASD probands Cohort ASD PRS (beta, p-value) EA PRS (beta, p-value) SCZ PRS (beta, p-value) SSC Probands 0.072, 1.28E , 6.57E , 1.89E-02 (n = 2,584) PGC ASD 0.065, 4.08E , 1.00E , 2.44E-03 Probands (n = 3,870) SSC+PGC ASD Probands (n = 6,454) 0.068, 1.79E , 1.76E , 1.38E-04 For each of the three cohorts, we performed a single logistic regression predicting proband (1) or mid-parent (0) status from each of the three PRS; p-values estimate the probability with which the mid-parent and proband means are equal, controlling for the other two PRS. 18

31 Supplementary Table 19. IQ effect of ASD-associated genetic risk factors Genetic correlation with IQ in the general population (r, p-value), from Hagenaars et al. 9 ASD IQ associations (beta, p-value) ASD PRS EA PRS SCZ PRS CDNV 0.187, , 2.0E , 3.5E-11 NA 0.45, , , , 1.45E-05 The three ASD IQ - PRS associations are from three linear regressions predicting full-scale proband IQ from each PRS, controlling for proband sex and the first 10 principal components of proband ancestry; the ASD IQ CDNV association is from a linear regression predicting full-scale proband IQ from CDNV presence/absence, controlling for proband sex; all four associations were performed in genotyped and sequenced European ancestry Simons Simplex Collection probands (n = 1,674); p-values estimate probability of no association between genetic factor (polygenic risk or genetic correlation) and IQ; genetic correlation results from Hagenaars et al. 9 19

32 Supplementary Table 20. Sibling-based ptdt is less statistically powered than parent-based ptdt ASD PRS (ptdt deviation mean (SD), p-value) SSC Sibling ptdt (1.022), 1.81E-04 SSC Parent ptdt (0.978), 3.83E-10 EA PRS (ptdt deviation mean (SD), p-value) (0.769), 6.06E (0.662), 5.01E-07 SCZ PRS (ptdt deviation mean (SD), p-value) (0.470), 5.54E (0.361), 3.54E-07 Sibling and parent comparisons performed with same cohort (n = 2,091 quads) to facilitate comparison; P-values denote the probability that the mean of the ptdt deviation distribution is 0 (two-sided, one-sample t test). 20

33 Supplementary Table 21. CNV analysis integrating parental age y Case status (proband = 1, 0 = unaffected sibling) x1 Constrained and/or 500 kb CNV deletion Constrained CNV deletion Unconstrained 500 kb CNV deletion Unconstrained and < 500 kb CNV deletion CNV duplication with gene CNV duplication without a gene No parental age controls (n = 2,587 cases) (n = 2,100 controls) Controlling for paternal and maternal age at birth of child (n = 2,346 cases) (n = 1,761 controls) OR p-value OR p-value E E E E NA NA E E All variants are de novo; constrained refers to CNVs containing genes that are intolerant of heterozygous loss of function variation (probability of being loss-of-function intolerant (pli) 0.9); NA denotes an analysis where all control carriers were missing parental age data; analytic model was logistic regression predicting proband/control status from count of CNVs; ORs are interpreted as the increased likelihood of proband status given presence of a variant; p-values test the null hypothesis that the OR is equal to 1 (no association between variant and case status). 21

34 Supplementary Table 22. Relationship between proband IQ, CDNV status and mid-parent PRS Proband CDNV status (n = 1,677) Proband FSIQ (controlling CDNV status) (n = 1,674) Mid-parent ASD PRS (beta, p-value) Mid-parent EA PRS (beta, p-value) Mid-parent SCZ PRS (beta, p-value) 0.081, , E-04, , , , For each polygenic risk category, we performed a linear regression predicting mid-parent PRS from proband CDNV status (presence = 1, absence = 0), and next a linear regression predicting mid-parent PRS from proband full-scale IQ and CDNV status; in the first row, p-values indicate the probability of no association between CDNV status and mid-parent PRS; in the second row, p-values indicate the probability of no association between proband FSIQ and midparent PRS, controlling for proband CDNV status; analytic cohort is Simons Simplex Collection European ancestry families with probands who were both genotyped and sequenced and genotyped parents; FSIQ = full-scale IQ. 22

35 Supplementary Note Glossary ASD Proband An individual diagnosed with autism spectrum disorder ASD PRS Polygenic Risk Score for Autism Spectrum Disorder BMI PRS Polygenic Risk Score for Body Mass Index CDNV Contributing de novo variant CNV Copy number variant (deletion or duplication) EA PRS Polygenic Risk Score for Educational Attainment ipsych-broad Autism Group The Lundbeck Foundation Initiative for Integrative Psychiatric Research-Broad Institute Autism Group Mid-Parent PRS Average polygenic risk score of mother and father in a given family PGC ASD Psychiatric Genomics Consortium Autism Group pli Probability of being Loss-of-Function Intolerant (probability that gene is intolerant of heterozygous loss-of-function variation) 10 PRS Polygenic Risk Score ptdt Polygenic transmission disequilibrium test PTV Protein-truncating variant (frameshift, splice acceptor, splice donor, nonsense) SCZ PRS Polygenic Risk Score for Schizophrenia SSC Simons Simplex Collection 23

36 Estimates of assortative mating on polygenic risk. We examined evidence for assortative mating by correlating maternal and paternal polygenic risk for each trait in both SSC and PGC ASD. We restricted our analysis to families of European ancestry (Online Methods: Sample Description) to avoid ancestral confounding. For each of ASD, EA and SCZ PRS, we regressed out the first 10 principal components of ancestry of each parent and correlated the residuals between mothers and fathers (Supplementary Table 4). Parent PRS as a function of parent sex. We analyzed whether mothers and fathers differed with regard to average ASD, SCZ, or EA PRS. In each of European ancestry SSC and PGC ASD cohorts (Online Methods: Sample Description), we performed three linear regressions, each predicting polygenic risk for ASD, EA and SCZ from parent sex while controlling for the first 10 principal components of each parent s ancestry (Supplementary Table 6). Mid-Parent PRS as a function of proband sex. We analyzed whether mid-parent PRS differed as a function of proband sex (European ancestry only). In each of SSC and PGC ASD, we performed three linear regressions, predicting mid-parent polygenic risk for ASD, EA and SCZ from proband sex, controlling for the first 10 principal components of proband ancestry (Supplementary Table 7). European ancestry ptdt. We repeated ptdt for ASD, EA and SCZ PRS in the four European ancestry cohorts defined in the Online Methods: European SSC probands (n = 1,851), European SSC unaffected siblings (n = 1,509), European PGC probands (n = 3,209), and the combination of European SSC and European PGC probands (n = 5,060). Polygenic transmission before and after ancestry restriction was largely consistent (Supplementary Table 8). In the European ancestry ptdt, there were no significant differences in ptdt deviation across the polygenic risk categories (P > 0.05 for all comparisons) (Supplementary Figure 2). Without ancestry restriction (Figure 1a), the mean ASD and EA ptdt deviation values were significantly greater than the mean SCZ ptdt deviation value (P < for SSC+PGC ASD proband cohort). The SCZ PRS is most stratified by ancestry (Supplementary Figure 3), and limiting the ptdt analysis to families of European ancestry reduced the variance of the mid-parent SCZ PRS distribution. As the ptdt deviation value was normalized by the standard deviation of the mid-parent PRS, the mean proband deviation from the midparent value appeared larger in the European ancestry SCZ analysis than without an ancestry filter (P = 3.10E-04); if the deviations were not standardized by mid-parent PRS, this difference was eliminated (P = 0.89). This suggested no difference in ptdt deviation effect sizes for ASD, EA and SCZ PRS after controlling for ancestral effects. Body Mass Index Polygenic Risk. To identify the optimal p-value threshold for polygenic risk scoring, we first calculated polygenic risk for all of the SSC at the ten standard p-values thresholds (Online Methods: Polygenic Risk Scoring). We then associated the resulting polygenic risk scores with reported body mass index (BMI) in the SSC (BMI = Weight/Height 2 ). To do so, we identified the European ancestry SSC subcohort (Online Methods: Sample Description) and regressed out the first 10 principal components of ancestry from each individual s polygenic risk scores. We also removed SSC individuals with BMI at least 3 standard deviations from the cohort mean. We then correlated the BMI of the remaining 24

37 individuals with their polygenic risk scores, and identified P = 0.2 as the threshold that resulted in the strongest association (r = 0.14, P = 8.68E-09). Sibling ptdt. We performed a sibling-based ptdt analysis to compare its statistical power with that of the parent-based ptdt. Using genotyped SSC quads (n = 2,091), we calculated sibling ptdt deviation as follows: As this analysis was specific to SSC, we generated polygenic risk scores using info thresholds from SSC imputation. For comparison of statistical power, we performed parent ptdt in the same cohort of quads (Supplementary Table 20). The loss of statistical power in the sibling-based ptdt was due to the increased variance of the distribution of sibling PRS relative to mid-parent PRS. The mid-parent distribution has reduced variance due to averaging of parent values. De novo duplications. Duplications of constrained genes (pli 0.9) were not associated with ASD risk after controlling for duplication size and maternal age at birth of child (P = 0.92, logistic regression). However, pli may not be a good indicator of genes that are sensitive to duplication. Duplications may result in gain of function, or in other changes that do not result in loss of function, but increase risk for ASDs. Association between co-occurring neurodevelopmental outcomes and proband sex ratio. We first calculated an expectation for the male:female ratio (6.42) as the total count of male SSC probands (n = 2,029) over the total count of female SSC probands (n = 316) (cohort: SSC probands both sequenced and genotyped). Next, we calculated the observed male:female ratio of CDNV carriers within each of the four categories of co-occurring neurodevelopmental outcomes (Supplementary Table 16). We used Fisher s exact tests to determine the significance of the difference between expected and observed male:female ratio in each category. The observed male:female ratio was significantly lower than expected for probands with at least one co-occurring neurodevelopmental phenotype (P < 5.00E-03). ptdt in expanded set of CDNVs. We expanded our ptdt analysis by examining whether ASD associated risk was over inherited by carriers of a broader set of de novo mutations (cohort: genotyped and sequenced SSC, n = 2,346). Our expanded de novo mutation set included constrained PTVs (not observed in ExAC, pli 0.9) and all de novo copy number variants (deletions and duplications) (n = 318 probands with 1 variant) (Supplementary Table 13). We also conducted ptdt in SSC genotyped and sequenced probands with full-scale IQ < 70 who lacked any de novo PTV or CNV (Supplementary Table 13). Relationship between mid-parent PRS, proband IQ, and CDNV status (Supplementary Table 22). Next, we analyzed whether mid-parent PRS varied as a function of whether the proband carried a contributing de novo variant (CDNV, Online Methods: De novo variant analyses). Our analytic cohort was genotyped and sequenced SSC families with a European ancestry-defined proband (n = 1,677). A subset of these families had a proband with at least 25

38 one CDNV (n = 161 probands). We performed three linear regressions with CDNV status and first 10 proband principal components of ancestry as the independent variables, and mid-parent PRS for ASD, EA and SCZ as the dependent variables. Finally, we analyzed whether mid-parent PRS varied as a function of proband IQ, controlling for whether the proband carried a CDNV. Our analytic cohort was genotyped and sequenced SSC families with a European ancestry-defined proband and IQ assessment available (full scale IQ) (n = 1,674). A subset of these families had a proband with at least one contributing de novo event (n = 161). We performed three linear regressions with proband IQ, CDNV status and first 10 proband principal components of ancestry as independent variables, and mid-parent PRS as the dependent variable. 26

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Nature Genetics: doi: /ng Supplementary Figure 1. PCA for ancestry in SNV data.

Nature Genetics: doi: /ng Supplementary Figure 1. PCA for ancestry in SNV data. Supplementary Figure 1 PCA for ancestry in SNV data. (a) EIGENSTRAT principal-component analysis (PCA) of SNV genotype data on all samples. (b) PCA of only proband SNV genotype data. (c) PCA of SNV genotype